Hm, despite adding reaver binary to /home/user/.reaver/ and restarting Cleven, (I think Cleven recognized it, as now it shows "Reaver" button - before that, button was absent) as soon as I use Reaver button, empty terminal window pops up and closes.

As for icon, rebooting doesn't solve the problem (and it shouldn't, as for quite some time hildon-desktop is refreshed upon installation of new packages. At least, using fapman). Yet, changing Icon line in cleven.desktop to:
... Solves the issue (partially, is it's shown properly in desktop, but not in menu). I have no idea why - icon is indeed sitting on 64x64/apps.

/Estel